Non-invasive cardiac output determination

ABSTRACT

A method of controlling a gas delivery apparatus including an apparatus controllable variable using an iterative algorithm to deliver a test gas (TG) for non-invasively determining a subject&#39;s pulmonary blood flow comprising iteratively generating and evaluating test values of a iterated variable based on an iterative algorithm in order output a test value of the iterated variable that meets a test criterion wherein iterative algorithm is characterized in that it defines a test mathematical relationship between the at least one apparatus controllable variable, the iterated variable and an end tidal concentration of test gas attained by setting the apparatus controllable variable, such that the iterative algorithm is determinative of whether iteration on the test value satisfies a test criterion or iteratively generates a progressively refined test value.

FIELD OF THE INVENTION

The present invention relates to a novel method for non-invasivelymeasuring pulmonary blood flow, to a novel method for controlling a gasdelivery apparatus and to a system and apparatus for implementing themethods.

BACKGROUND OF THE INVENTION

Many methods have been developed which attempt to measure pulmonaryblood flow without invasive access to the circulation ({dot over (Q)}).These methods, and their corresponding limitations, have beenexhaustively reviewed in the literature [1]. What emerges from thesereviews, however, are the potential benefits of non-invasive pulmonaryblood flow monitoring and the current lack of an adequate method.

Fick described the relationship between the blood gas concentrations andthe minute volume of expired gases during steady state [2].Specifically, if the amount of CO₂ in the lung is not changing, the fluxof CO₂ between the pulmonary capillary blood and the alveolar space isequal to the minute volume of expired CO₂ ({dot over (V)}CO₂). The fluxof CO₂ between the blood and the lungs can be calculated from theproduct of the pulmonary blood flow and the difference between the CO₂concentration in the mixed-venous blood (C vCO₂) entering the pulmonarycirculation and the corresponding concentration in the arterializedblood (CaCO₂) leaving the pulmonary circulation. The Fick mass balancerelation is shown in equation 1.

{dot over (V)}CO₂={dot over (Q)}(C v CO₂—CaCO₂)  (eq. 1)

If the steady state minute volume of expired CO₂, arterial CO₂concentration, and mixed-venous CO₂ concentration can be determined,then the pulmonary blood flow can be calculated from equation 1.Conventionally, the minute volume of expired CO₂ is calculated from bagcollection of the expired breath, the product of the minute ventilationand the concentration of CO₂ in the mixed-expired gas, or integration ofthe instantaneous concentration of CO₂ at the mouth weighted by theinstantaneous flow. The partial pressure of CO₂ in the arterial blood isassumed to be equal to the end-tidal partial pressure of CO₂ and thenconverted to a concentration via the CO₂ dissociation curve ofoxygenated whole blood [3,4]. Traditionally, two methods have been usedto estimate the mixed-venous concentration of CO₂ for the purpose ofpulmonary blood flow measurement. The first method was presented byDefares [5]; the method of Collier [6] was published shortly thereafter.

In the method described by Defares, rebreathing is executed from a bagwith a low initial concentration of CO₂. As rebreathing proceeds, thelevel of CO₂ in the bag and the lung exponentially approach that in themixed-venous blood. However, equilibration of the bag and the lung withthe mixed-venous blood is slow as the volume of gas in the functionalresidual capacity is large. As a result, equilibration does not usuallyoccur before the change in the arterial CO₂ induced by rebreathingrecirculates back to the lung. The steady state mixed-venous CO₂—theasymptote of the exponential rise in end-tidal CO₂—must therefore becalculated from fitting an exponential curve to the end-tidal CO₂ of thebreaths during rebreathing prior to recirculation.

In the method introduced by Collier, rebreathing is executed from a bagwith an initial concentration of CO₂ slightly above an estimatedmixed-venous CO₂ concentration. The initial CO₂ in the bag is intendedto, upon inhalation, eliminate the CO₂ diffusion gradient between thefunctional residual capacity and the mixed-venous blood on the firstbreath of rebreathing. The equilibrium between the mixed-venous bloodand the alveolar space is recognized by the presence of a plateau in theend-tidal CO₂ during rebreathing.

As a variant of these rebreathing methods, Gedeon described a partialCO₂ rebreathing method for measuring pulmonary blood flow [7]. Partialrebreathing differs from the full rebreathing methods of Defares andCollier in that the entire tidal volume is not composed of rebreathedgas. Partial rebreathing is implemented by introducing a serial deadspace into the breathing circuit to increase the volume of rebreathedgas in each breath [8].

Partial rebreathing increases the average CO₂ content of the inspiredgas so that the flux of expired CO₂ is reduced. As a result, thealveolar and arterial CO₂ concentrations rise towards the level at whichthe flux of CO₂ between the blood and the lung will once again equal theexpired flux. Like the method of Defares, equilibration duringrebreathing may not occur before recirculation. Nevertheless, the Fickmass balance relation is applied at the end of rebreathing as shown inequation 2.

{dot over (V)}CO′₂={dot over (Q)}(C v CO₂—CaCO′₂)  (eq. 2)

Two steady states can be solved for the pulmonary blood flow and themixed-venous concentration of CO₂, revealing the differential Fickequations shown in equations 3a1 and 3b1.

$\begin{matrix}{\overset{.}{Q} = \frac{{\overset{.}{V}{CO}_{2}^{\prime}} - {\overset{.}{V}{CO}_{2}}}{{CaCO}_{2} - {CsCO}_{2}^{\prime}}} & \left( {{{eq}.\mspace{14mu} 3}{a1}} \right) \\{{C\; \overset{\_}{v}{CO}_{2}} = \frac{{{{CaCO}_{2} \cdot \overset{.}{V}}{CO}_{2}^{\prime}} - {{{CaCO}_{2}^{\prime} \cdot \overset{.}{V}}{CO}_{2}}}{{\overset{.}{V}{CO}_{2}^{\prime}} - {\overset{.}{V}{CO}_{2}}}} & \left( {{{eq}.\mspace{14mu} 3}{b1}} \right)\end{matrix}$

In practice, fluctuations in alveolar ventilation induce perturbationsin the instantaneous flux of expired CO₂ and in arterial CO₂ levels,leading to significant errors in calculating pulmonary blood flow. Thiserror is pronounced in untrained spontaneous breathers [9].

In the method of Defares specifically, the mixed-venous concentration ofCO₂ is extrapolated from the exponential rise in the end-tidal CO₂measured during rebreathing before recirculation. However, the number ofbreaths available for calculating the exponential asymptote is limited,and as a result, determination of the mixed-venous CO₂ is highlysensitive to errors in the end-tidal measurements.

Alternatively, in the method of Collier, the mixed-venous CO₂concentration is measured, but equilibration of the lung with themixed-venous CO₂ before recirculation depends on the initial volume andcomposition of the gas in the rebreathing bag. The optimal startingconditions vary with the subject's mixed-venous concentration of CO₂ andfunctional residual capacity so that, in practise, an effective startingvolume and concentration is determined by trial-and-error in repeatedexecutions of the rebreathing manoeuvre until a plateau is observed inthe end-tidal record [6].

In partial rebreathing methods, the last breath of the rebreathing phaseis assumed to represent the second steady state conditions required tocalculate the pulmonary blood flow. However, where the rebreathingperiod is short, equilibrium is not achieved; and, where the rebreathingperiod is long recirculation confounds the measurement [10].

Therefore, although measuring pulmonary blood flow ({dot over (Q)})should be an integral part of clinical monitoring and physiologicalresearch, it is not routinely implemented because of the invasiveness,cost, or inaccuracy of existing methods. To be of the greatest utility,a pulmonary blood flow monitor must provide accurate, rapid, andrepeatable measurements over a broad range of physiological andpathological conditions.

SUMMARY OF THE INVENTION

We have developed a novel system for non-invasively measuring thepulmonary blood flow that implements an iterative respiratory algorithmand thereby overcomes the limitations of previous methods. The methodcan be adapted to an automated system for non-invasively measuringpulmonary blood flow that provides for reliable monitoring of pulmonaryblood flow in a wide range of subjects and environments. According toone aspect, the invention is directed to a method of controlling a gasdelivery apparatus to deliver a test gas (TG) for non-invasivelydetermining a subject's pulmonary blood flow comprising the steps of:

-   -   (a) Controlling at least one apparatus controllable variable to        test one or more test values for an iterated variable in an        iterative algorithm by:        -   A) providing an inspired concentration of a test gas that            achieves a test concentration of the test gas in the            subject's end tidal exhaled gas;        -   B) using a test value of an iterated variable in an            iterative algorithm to set the gas delivery apparatus to            deliver, for at least one series of inspiratory cycles, an            inspiratory gas comprising a test gas that is computed to            target the test concentration of the test gas based on a            test value of the iterated variable;        -   C) obtaining input comprising measurements of a measurable            variable for at least one series of inspiratory cycles,            optionally end tidal concentrations of test gas for            expiratory cycles corresponding to the at least one series            of inspiratory cycles;        -   D) using at least one measurement obtained in step C) as a            reference end tidal concentration value to generate at least            one of the following outputs:            -   (1) a test value satisfies the test criterion;            -   (2) a refined test value;            -   wherein the reference end tidal concentration is a                surrogate steady state value and is used to generate the                refined test value;    -   (b) If output (1) is not obtained, repeating step (a) as        necessary at least until output (1) is obtained; and    -   (c) If output (1) is obtained, outputting a value for pulmonary        blood flow which, based on the test criterion, sufficiently        represents a subject's true pulmonary blood flow.

As described below, obtaining steady state values for at least oneapparatus controllable variable and an end tidal concentration of testgas for or as part of the test is central to exploiting key testmathematical relationships that may be employed in the iterativealgorithm. The rate of flow of inspiratory gas into the breathingcircuit, when determinative of alveolar ventilation can be used tocompute a minute volume of expired test gas. A variety of othernon-invasive or invasive ways of obtaining these values are known. Thesevalues may conveniently be resting steady state values. Therefore, whileit is not necessary to employ the invention to obtain these values, theyare employed in the execution of the iterative algorithm or for thealgorithm. Hence, according to a preferred embodiment of the invention,initial steady state values are obtained within or for the iterativealgorithm. For convenience, this stage of gathering input of steadystate values for the iterative algorithm is referred to as the baselinephase.

According to another aspect, the invention is directed to a method fornon-invasively determining pulmonary blood flow comprising obtainingsteady state values for minute volume of expired test gas and end tidalconcentration of test gas and implementing steps (a) to (c) as definedabove, the method adapted to be implemented by a gas delivery apparatusas defined herein. The method can be executed rapidly and isnon-therapeutic in nature. The method may be carried out as apreliminary step to obtaining a diagnosis in which obtaining pulmonaryblood flow is useful for the ensuing diagnosis or forms part of abroader diagnostic work-up.

According to yet another aspect, the invention is directed to a gasdelivery system adapted to deliver a test gas (TG) for non-invasivelydetermining a subject's pulmonary blood flow comprising:

A gas delivery apparatus;

A control system for controlling the gas delivery apparatus based on aniterative algorithm including controlling at least one apparatuscontrollable variable to test one or more test values for an iteratedvariable, the control system comprising a computer, the gas deliverysystem including means for

-   -   A) Obtaining input of steady state values sufficient for input        into the differential Fick equation, optionally minute volume of        expired test gas and an end tidal concentration of test gas;    -   B) Obtaining input of a test concentration of the test gas in        the subject's end tidal exhaled gas wherein the test        concentration of test gas is achieved by administration of a        test gas bolus;    -   C) Using a test value of the iterated variable in an iterative        algorithm to set a gas delivery apparatus to deliver, for at        least one series of inspiratory cycles, a test gas that is        computed to maintain the test concentration of the test gas;    -   D) Obtaining input comprising measurements of end tidal        concentrations of test gas for expiratory cycles corresponding        to the at least one series of inspiratory cycles;    -   E) using at least one measurement obtained in step D) as a        reference end tidal concentration value to generate at least one        of the following outputs:        -   (1) the test value satisfies the test criterion;        -   (2) a refined test value;    -   wherein the reference end tidal concentration is a surrogate        steady state value and is used to generate the refined test        value;    -   wherein the control system is adapted to iteratively test a        series of test values for the iterated variable based on the        following criteria:    -   If output (1) is not obtained, repeating step (B) to (E) as        necessary at least until output (1) is obtained; and    -   If output (1) is obtained, outputting a value for pulmonary        blood flow which, based on the test criterion, sufficiently        represents a subject's true pulmonary blood flow.

The computer, as broadly defined herein is understood to supply all thenecessary components that are not contained with the gas deliveryapparatus. Optionally, a separate CPU runs program code used to controla gas delivery apparatus comprising one or more conventional componentsof a gas blender. The gas delivery apparatus may be operativelyconnected to one or more gas analyzers including a gas analyzer for thetest gas. The gas delivery apparatus is optionally operativelyassociated with a pressure transducer as described below. The computerreceives inputs from one or more input devices for inputting values forvarious test parameters and values described herein and inputs from thegas analyzer and pressure transducer and provide outputs to suitableflow controllers and a computer readout for example a screen to outputof key parameters and values described herein, including preferably avalue for pulmonary blood flow.

The iterated variable is preferably pulmonary blood flow and optionallymay be an iterated variable determined by pulmonary blood flow fromwhich pulmonary blood flow may be calculated. For example, depending onthe choice of test gas, the iterated variable may be the mixed venousconcentration of the test gas.

The iterative algorithm is characterized in that it defines amathematical relationship between the at least one apparatuscontrollable variable, the iterated variable and a measurable variable,optionally the end tidal concentration attained by setting the apparatuscontrollable variable, such that the iterative algorithm isdeterminative of whether iteration on the test value satisfies a testcriterion.

The iterative algorithm preferably employs a test mathematicalrelationship based on the Fick equation and differential Fick equation.The iterative algorithm optionally employs equation 5 or 5-0.

The iterative algorithm may be based on the Fick or differential Fickequation.

The at least one apparatus controllable variable is optionally acontrollable inspired concentration of test gas in the inspiratory gas.

The at least one apparatus controllable variable is optionally acontrollable rate of flow of test gas-containing inspiratory gas intothe breathing circuit such that the rate of flow is indicative of ordeterminative of the alveolar ventilation, as described below.

The apparatus controllable variable may be both a selectable inspiredconcentration of test gas in the inspiratory gas and the rate of flow ofthe inspiratory gas into the breathing circuit For convenience, theapparatus controllable variable is preferably a selectable inspiredconcentration of test gas in the inspiratory gas which targets the testconcentration of test gas in the end tidal gas obviating the need tochange the rate of flow of inspiratory gas set for the test.

The iterative algorithm may in one embodiment rely on equation 5 or 5-0as the test mathematical relationship which is based on the Fickequation to solve for an the inspired concentration of test gas in theinspiratory gas which targets the test concentration of test gas in theend tidal gas. The equation may be equation 7a or 7a-0 as defined below.These equations pertain to CO₂ as a test gas but may be generalized toanother test gas. Inputs in equation 7a and 7a-0 may be obtained fromequations 6a and 6b, and 6a-0/6b-0, respectively, which may also begeneralized to another test gas where the relationship between end tidaland arterial values is established or readily ascertained.

The iterative algorithm may rely on equation 5 or 5-0 to solve for arate of flow of inspiratory gas into the breathing circuit which targetsthe test concentration of test gas in the end tidal gas. The equationmay be equation 7b or 7b-0 as defined below. These equations pertain toCO₂ as a test gas but may be generalized to another test gas where therelationship between end tidal and arterial values is established orreadily ascertained. Inputs in equation 7b and 7b-0 may be obtained fromequations 6a and 6b, and 6a-0/6b-0, respectively, which may also begeneralized to another test gas where the relationship between end tidaland arterial values is established or readily ascertained.

The at least one apparatus controllable variable is optionally the rateof flow of test gas-containing inspiratory gas into the breathingcircuit such that the rate of flow is determinative and reliablyindicative of the alveolar ventilation. For example, the alveolarventilation of a subject that is paralyzed and not making an independentinspiratory effort may be controlled by a ventilator setting.

Preferably the rate of flow of test gas-containing inspiratory gas intothe breathing circuit is determinative of the alveolar ventilation,optionally wherein the fresh gas flow is set to be equal to or less thanthe minute ventilation and the balance of the subject's inspiratoryrequirements are made up by a neutral gas, [11] for example re-breathedgas.

Optionally, the breathing circuit is a sequential gas delivery circuitwhich allows a subject to re-breath expired end tidal gas when the flowof gas into the breathing circuit is set to be equal to or less than theminute ventilation. The circuit may organize passive access to therebreathed gas. The flow of gas may be set to fill an inspiratoryreservoir which the subject can then deplete in each inspiratory cycle,whereupon negative pressure in the circuit triggers access to are-breathed gas until the end of inspiration.

Optionally, the refined test value is ascertained based on thedifferential Fick equation (eq. 3a1 or 3b1), by using steady statevalues of VCO2 and CaCO2, optionally resting steady state valuesobtained prior to establishing a test concentration of test gas in theend tidal gas. These values are important inputs into other equations aswell. In this manner, the reference end tidal concentration is used togenerate a refined test value for the iterated variable. Alternatively,the estimate can be refined based on an estimate obtained usingequations 3a2 or 3b2 as described below.

The “test concentration” of the test gas is the arterial concentrationof test gas following administration a test gas bolus as reflected inthe end tidal gas following the inspiratory cycle in which the test gasbolus is administered. A test gas bolus is one which achieves aphysiologically compatible test concentration of the test gas in thearterial circulation, and increases the concentration of the test gassufficiently to make the iterative testing of test values (one or moresuccessive test values) accurate having regard to the test criterion andthe speed/accuracy of the gas delivery apparatus and gas sensor used tomeasure the end tidal concentration values. Optionally, when using asequential gas delivery circuit to perform the test, a testconcentration of test gas may be administered by reducing theinspiratory flow in a manner (e.g. setting the flow to 0 for one breath)in which the test gas bolus is constituted by exhaled gas, for example,where the test gas is carbon dioxide a gas having a higher concentrationof carbon dioxide.

The test criterion optionally serves to define an acceptable differencebetween the reference end tidal concentration of test gas and the testconcentration of test gas, which establishes that a test value or arefined test value is acceptably close to a value from which the truepulmonary blood flow can be ascertained. The test criterion may also beto iterate a defined number of times. The test criterion may be tocontinue the iteration indefinitely by fixing this outcome (e.g. bydetermining that satisfaction of the test criterion is false).

Therefore, according to one embodiment, the invention is directed to amethod of controlling a gas delivery apparatus to deliver a test gas(TG) for non-invasively determining a subject's pulmonary blood flowcomprising the steps of:

-   -   (a) Controlling the flow of an inspiratory gas comprising a test        gas into a breathing circuit, wherein the concentration of the        test gas in the inspiratory gas (FiTG_(g1)) or the rate of flow        of gas into the circuit is adjusted to test one or more test        values for a iterated variable selected from the group        comprising pulmonary blood flow or mixed venous test gas        concentration (C vTG) by:        -   A) obtaining input of a steady state end tidal concentration            and at least one corresponding apparatus controllable            variable        -   B) providing an inspired concentration of a test gas that            achieves a test concentration of the test gas in the            subject's end tidal exhaled gas;        -   C) using a test value of an iterated variable in a test            mathematical relationship to set the gas delivery apparatus            to deliver, for at least one series of inspiratory cycles, a            test gas that is computed to maintain the test concentration            of the test gas;        -   D) obtaining input comprising measurements of end tidal            concentrations of test gas for expiratory cycles            corresponding to the at least one series of inspiratory            cycles;        -   E) using at least one measurement obtained in step D) as a            reference end tidal concentration value to generate at least            one of the following outputs:        -   (1) the test value satisfies the test criterion;        -   (2) a refined test value, wherein the reference end tidal            concentration is a surrogate steady state value and is used            to generate the refined test value;    -   (b) If output (a) is not obtained, repeating step (a) as        necessary until output (1) is obtained; and    -   (c) If output (1) is obtained, outputting a value for pulmonary        blood flow which, based on the test criterion, that sufficiently        represents a subject's true pulmonary blood flow.

Optionally, the reference end tidal concentration is the last end tidalconcentration value obtained prior to a recirculation or an average ofthe last end tidal concentration values.

According to another aspect, the invention is directed to a method fornon-invasively determining a subject's pulmonary blood flow comprisingthe steps of:

-   -   (a) Controlling the flow of an inspiratory gas comprising a test        gas into a breathing circuit, wherein the concentration of the        test gas in the inspiratory gas (FiTG_(g1)) or the rate of flow        of gas into the circuit is adjusted to test one or more test        values for a iterated variable selected from the group        comprising pulmonary blood flow or mixed venous test gas        concentration (C vTG) by:        -   A) obtaining input of a steady state end tidal concentration            and a corresponding value of at least one apparatus            controllable variable;        -   B) providing an inspired concentration of a test gas that            achieves s a test concentration of the test gas in the            subject's end tidal exhaled gas;        -   C) using a test value of an iterated variable in a test            mathematical relationship to set the gas delivery apparatus            to deliver, for at least one series of inspiratory cycles, a            test gas that is computed to maintain the test concentration            of the test gas;        -   D) obtaining input comprising measurements of end tidal            concentrations of test gas for expiratory cycles            corresponding to the at least one series of inspiratory            cycles;        -   E) using at least one measurement obtained in step C) as a            reference end tidal concentration value to generate at least            one of the following outputs:        -   (3) the test value satisfies the test criterion;        -   (4) a refined test value, wherein the reference end tidal            concentration is a surrogate steady state value and is used            to generate the refined test value;    -   (b) If output (a) is not obtained, repeating step (a) as        necessary until output (1) is obtained; and    -   (c) If output (1) is obtained, outputting a value for pulmonary        blood flow which, based on the test criterion, that sufficiently        represents a subject's true pulmonary blood flow.

According to optional embodiments of a method as defined above:

-   1. the test gas is carbon dioxide;-   2. a subject's consumption of the test gas containing inspiratory    gas is controlled to define the subject's alveolar ventilation (the    minute volume of gas which reaches the alveoli and may participate    in gas exchange).-   3. the subject's alveolar ventilation is defined by setting the rate    of flow of a test gas containing gas into a breathing circuit to be    equal to or less than the subject's minute ventilation and    delivering to the subject on inspiration, the test gas containing    inspiratory gas and when the test gas is depleted for a breath, for    the balance of that breath, a neutral (for example re-breathed) gas.

According to another aspect the invention is directed to an inspiratorygas delivery system for non-invasively determining pulmonary blood flowcomprising:

(a) A gas delivery apparatus;

(b) A control system for controlling the gas delivery apparatusincluding:

-   -   Means for obtaining input of:        -   a. a steady state value of an end tidal concentration of a            test gas and a corresponding value for at least one            apparatus controllable variable;        -   b. a test concentration of a test gas in the subject's end            tidal gas;        -   c. test value for an iterated variable for input into an            iterative algorithm;        -   d. a test criterion;        -   e. a reference end tidal concentration representing a            surrogate steady state value;    -   Means for computing:        -   f. a value for at least one apparatus controllable variable,            said value computed by the iterative algorithm to maintain            the test concentration of test gas in the subject's end            tidal gas for a series of inspiratory cycles, the reference            end tidal concentration selected or computed from selected            measurements of end tidal concentrations of test gas for            expiratory cycles corresponding to the at least one series            of inspiratory cycles;        -   g. iteratively, where a previously computed test value does            not meet the test criterion, until a test criterion is met,            a refined test value for a iterated variable and a            corresponding value for an apparatus controllable variable            generated by the iterative algorithm for an ensuing series            of inspiratory cycles so as to provide a new reference end            tidal concentration for comparison to the then current            reference test concentration; and            -   means for outputting a test value for a iterated                variable that meets the test criterion.

Suitable sequential gas delivery circuits and related apparatusinformation are disclosed WO/2004/073779, WO/2002/089888 andWO/2001/074433.

To compute the apparatus controlled variable required to maintain thetest gas concentration in the end-tidal exhaled gas, the followinginputs are needed: the test gas concentration in the end-tidal exhaledgas to be maintained, and a steady state end tidal test gasconcentration and a corresponding value of at least one apparatuscontrollable variable. To refine the estimate of the test value, thefollowing inputs are needed: a steady state end tidal test gasconcentration and a corresponding value of at least one apparatuscontrollable variable, and a reference end tidal test gas concentrationand a corresponding value of at least one apparatus controllablevariable.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 is a schematic representation of one embodiment of a gas deliverysystem according to the invention.

FIG. 2, commencing at 2-1 and continuing as FIG. 2-2, is a table(Table 1) setting out a list of abbreviations used to express themathematical relationships employed in the description of severalembodiments of the invention described herein.

FIGS. 3 a, 3 b and 3 c are tables listing the various mathematicalrelationships employed in the description of embodiments of theinvention described herein.

FIG. 4 is a flowchart describing an iterative algorithm employed torecursively determine pulmonary blood flow according to a preferredembodiment of the invention.

FIG. 5 a (Panel A) is a series of a graphical depictions of iterationsof the iterative algorithm in which the effect on maintaining a testconcentration of test gas for different test values for pulmonary flowis depicted.

FIG. 5B (Panel B) is a graphical depiction of the effect ofover-estimating, under-estimating and correctly estimating a test valuefor a test variable, in this case, pulmonary blood flow.

DETAILED DESCRIPTION OF THE INVENTION

The term “reference end tidal concentration” is used to describe a valueobtained by measurement which reflects an arterial blood concentrationof the test gas preferably obtained prior to a recirculation time,preferably a value or one or more averaged values obtained closest intime to recirculation since this value may most usefully reflect a newsteady state value achieved as a result of administering the test gas.In this connection, it is noteworthy that although the differential Fickequation is a steady state equation, using reference end tidal test gasconcentrations obtained before a steady is reached does not prevent theadjusted test value for the iterated variable to be refined recursively.Therefore, the “reference end tidal concentration” is preferably atleast a “surrogate steady state value” i.e. a value preferably obtainedbefore a recirculation time that equals or sufficiently represents asteady state value to make the iterative process of meeting the testcriterion useful in practice. To reduce the number of iterationsrequired to determine pulmonary blood flow, the surrogate steady statevalue is preferably selected to be one value, or one or more averagedvalues, determined to be closest to a recirculation time—generally oneor more among the last test values obtained prior to a recirculation.Equation 9 may be used at each breath to detect recirculation of thearterial blood.

The term “refined test value” is used to refer to a value for a iteratedvariable that is revised relative a previous test value. Since theinvention contemplates that more than one iterated variable may beemployed and since the iterated variables are mathematicallyinterrelated the term refined test value should be understood to includea value indirectly derived from data related to a prior test valuerelated to another iterated variable.

The reference to an iterated variable which is determined by pulmonaryblood flow and from which pulmonary blood flow can be computed generallyrefers to a mixed venous test gas concentration. In contrast to carbondioxide, with respect to test gases such as oxyacetylene, which are notproduced or reliably consumed, the mixed venous blood concentration isequal to the arterial concentration at steady state and hence may notprovide useful information about the pulmonary blood flow. In this case,the choice of iterated variable for iteration of a test value would bepulmonary blood flow. If pulmonary shunt is known total pulmonary bloodflow can also be used to compute total cardiac output.

The term “gas delivery apparatus” means a device that can be controlledto control the rate of flow of the test gas into the circuit or set theconcentration of the test gas into the inspiratory gas, and preferablyboth, for example a respiratory gas blender known to those skilled inthe art, for example a gas blender with rapid flow controllers,optionally a gas blender capable of delivering accurate mixes of threegases into the circuit. The apparatus and gas mixes may of the typedescribed in published WO 2007/02197. The key functionality of theapparatus is understood to serve the role of establishing (byadministering test gas containing inspiratory gas) and maintaining atest concentration of test gas. The gas delivery apparatus may beoperatively associated with suitable gas analyzers to measure fractionalcarbon dioxide and oxygen concentrations at the mouth. The apparatus isoperatively associated with a control system for controlling the gasdelivery apparatus. The control system demands the required output ofthe gas delivery apparatus to maintain a test concentration of test gasin the manner described above. The control system or the apparatuscomprises the necessary controllers for this purpose as described above,for example for controlling rate of flow of inspiratory gas andoptionally separate flow controllers for controlling the rate of flow ofthe sources gases.

The gas delivery apparatus comprises at least one input port forreceiving a source which may be an inspiratory gas containing the testgas, at least one output port for connection to a breathing circuit anda flow controller for controlling the rate of flow of the inspiratorygas.

The flow controller optionally controls a gas delivery means.

The term “gas delivery means”, abbreviated refers to specifically tohardware for delivering (e.g. releasing, where the source gas is underpressure) specific volumes of a source gas comprising or consisting ofthe test gas for inspiration by the patient, preferably a device that isadapted to output volumes of variable incremental size. The gas deliverymeans may be any known gas delivery device such as a gas injector, or avalve, for example, a proportional flow control valve.

Optionally, the gas delivery apparatus is a gas blender, for example, anapparatus that comprises a plurality of input ports for connection to aplurality of gas sources in order to blend different gases that make upthe test gas containing gas, for example oxygen, air, nitrogen and atest gas. Optionally, carbon dioxide is the test gas. A flow controlleroptionally controls a proportional solenoid valve operatively associatedwith each gas source and optionally a separate flow controller and valveis employed to set the rate of flow of the blended gas into a breathingcircuit. Input devices are used to set the rate of flow of gas into thebreathing circuit and the concentration of the test gas in the gasprovided to the subject.

According to one aspect the invention is directed to a computer programproduct which implements a method according to the invention. Thecomputer program product comprises anon-transitory computer readablemedium encoded with program code for controlling operation of gasdelivery device, the program code including code for iterativelygenerating a series of test values of a iterated variable based on aniterative algorithm as described above in order to maintain a testconcentration of test gas. The program code may comprise code for:

-   -   A) providing an inspired concentration of a test gas that        defines a test concentration of the test gas in the subject's        end tidal exhaled gas;    -   B) using an iterative algorithm to set the gas delivery        apparatus to deliver, for at least one series of inspiratory        cycles, a test gas that is computed to target the test        concentration of the test gas based a test value of the iterated        variable;    -   C) obtaining input comprising measurements of end tidal        concentrations of test gas for expiratory cycles corresponding        to the at least one series of inspiratory cycles;    -   D) using at least one measurement obtained in step C) as a        reference end tidal concentration value to generate at least one        of the following outputs:    -   (1) the test value satisfies the test criterion;    -   (2) a refined test value;    -   wherein the reference end tidal concentration is a surrogate        steady state value and the refined test value is ascertainable        from the reference end tidal concentration;

The program code may include code to test a series of test values forthe iterated variable based on the following criteria:

-   -   If output (1) is not obtained, repeating step (A) to (D) as        necessary at least until output (1) is obtained; and    -   If output (1) is obtained, outputting a value for pulmonary        blood flow which, based on the test criterion, sufficiently        represents a subjects true pulmonary blood flow.

As described above, the computer readable medium or computer readablememory has recorded thereon computer executable instructions forcarrying out one or more embodiments of the above-identified methods.The invention is not limited by a particular physical memory format onwhich such instructions are recorded for access by a computer.Non-volatile memory exists in a number of physical forms includingnon-erasable and erasable types. Hard drives, DVDs/CDs and various typesof flash memory may be mentioned. The invention, in one broad aspect, isdirected to a non-transitory computer readable medium comprisingcomputer executable instructions for carrying out one or moreembodiments of the above-identified method.

The term “test concentration” means a concentration of a test gas in asubject's arterial blood as reflected in the end tidal concentration ofthe test gas in the subject's exhaled gas after attaining equilibriumwith that arterial concentration of test gas. As described above, thisconcentration is optionally achieved by arranging for a subject toobtain an inspiratory gas with any suitable concentration of test gaswhich may be delivered via the gas delivery apparatus or optionallyindirectly from a re-breathed gas.

The term “computer” is used broadly to refer to any device (constitutedby one or any suitable combination of components) which may used inconjunction with discrete electronic components to perform the functionscontemplated herein, including computing and obtaining input signals andproviding output signals, and optionally storing data for computation,for example inputs/outputs to and from electronic components andapplication specific device components as contemplated herein. Thecomputer may use machine readable instructions or dedicated circuits toperform the functions contemplated herein including without limitationby way of digital and/or analog signal processing capabilities, forexample a CPU, for example a dedicated microprocessor embodied in an ICchip which may be integrated with other components, for example in theform of a microcontroller. Key inputs may include input signals from agas analyzer, any type of input device for inputting inputs ascontemplate herein (for example, a knob, dial, keyboard, keypad, mouse,touch screen etc.) input from a computer readable memory etc. Keyoutputs include output of a control signal to control to a gas deliverymean such as a proportional control valve, for example outputs to a flowcontroller for controlling key components of gas delivery apparatus.

It is to be understood that an iterative algorithm may executecomputation based on a test mathematical relationship herein and thatthis relationships may be variously defined with equivalent formula inwhich terms/parameters are substituted by equivalent expressions thatare expressed in other forms or styles e.g. read from a graph etc. Hencethe invention is not limited by a reference to particular expressions ofa test mathematical relationship or related equations. For example,equation 5 may expressed by equivalent expressions of equation 1 fromwhich it is derived may be obtained by computing {dot over (V)}CO₂ (eq.4) in a manner other than expressed in equation 4. It is understood thatthe equations relate back to the Fick equation and differential Fickequation and hence a iterative algorithm expressed as being “based on”the Fick equation” is understood to be encompass equivalent expressionsor expansions of the equation with and without correction factors. Incontrast to prior methods, in one embodiment of a method according tothe invention, which is also primarily described hereafter in connectionwith using carbon dioxide as an embodiment of a “test gas”, theinvention contemplates obtaining steady state values optionally when thesubject is at “rest” and those values are stabilized. VCO₂ and CaCO₂ aremeasured in a first steady state. Rather than waiting for end-tidal CO₂to exponentially drift up to some second steady-value (which notably isgenerally not achieved before a recirculation), the present methodcontemplates giving a bolus of CO₂ to more acutely increase end-tidalCO₂ and calculate the inspired CO₂ required to force a second steadystate at the elevated end-tidal CO₂ from a guess at the cardiac output.If the end-tidal CO₂ remains stable, the guess at cardiac output wascorrect. If the guess at cardiac output was incorrect, much like in theprevious art, the end-tidal CO₂ will exponentially drift towards asteady state until recirculation. If we apply the differential Fickformula to our rest state and a second state represented for example bythe last test breath before recirculation, it is possible to calculate avalue for cardiac output. Much like previous methods, if the last testbreath doesn't actually represent steady state (i.e. equilibration didnot occur before recirculation), the cardiac output calculated by thedifferential Fick will be in error. However, it will be closer to theactual cardiac output than an original guess going in, and therefore,represents a refined estimate of the actual cardiac output. If thisprocedure is executed again, but with the refined estimate of cardiacoutput calculated from the last iteration, then there will be less driftduring the test, the last test breath will better represent steadystate, and again, our calculation of cardiac output will be even closerto the actual cardiac output. Repeat as necessary and the cardiac outputcalculated by this method will converge to the actual cardiac output.Accordingly, in contrast to prior methods there is no need to fitexponentials and extrapolate. In one embodiment, with sequential gasdelivery (SGD), it is possible to clamp alveolar ventilation, andtherefore measure a very consistent VCO₂ with equation 4 obviating theneed for simultaneous flow/CO₂ measurements. To implement the test, anoperator can provide a precise reduction in alveolar ventilation thatwill not be affected by changes in minute ventilation, and can thereforebe used in spontaneous breathers and mechanically ventilated subjects.

Iterative NICO Equations

A method according to the invention will now be described in accordancewith a preferred embodiment of the invention in which the test gas iscarbon dioxide.

With the use of sequential gas delivery, alveolar ventilation can becontrolled independent of overall minute ventilation. As a result,EQUATION 4 provides an accurate measure of the net minute volume ofexpired CO₂ calculated from the end-tidal fractional concentrations ofCO₂ and O₂ (FETCO₂, FETO₂) without the use of breath collection orflowmetry.

$\begin{matrix}{{\overset{.}{V}{CO}_{2}} = {{\overset{.}{V}}_{g\; 1} \cdot \frac{310}{\underset{\underset{BTPS}{}}{293}} \cdot \begin{bmatrix}{\underset{\underset{Haldane}{}}{\left( \frac{1 - {FICO}_{2,{g\; 1}} - {FIO}_{2,{g\; 1}}}{1 - {FETCO}_{2} - {FETO}_{2}} \right)} \cdot} \\{{FETCO}_{2} - {FICO}_{2,{g\; 1}}}\end{bmatrix}}} & {{EQUATION}\mspace{14mu} 4}\end{matrix}$

The correction term, BTPS, accounts for the expansion of gases in thelung owing to the increase in temperature from standard conditions. TheHaldane term applies the Haldane transform to calculate the expiredvolume when only the inspired volume is known.

When the amount of CO₂ in the alveolar space is unchanging, EQUATION 4can be substituted into EQUATION 1. The resulting steady state massbalance equation for the alveolar space is shown in EQUATION 5.

$\begin{matrix}{{{\overset{.}{V}}_{g\; 1} \cdot {\frac{310}{293}\begin{bmatrix}{\left( \frac{1 - {FICO}_{2,{g\; 1}} - {FIO}_{2,\; {g\; 1}}}{1 - {FETCO}_{2} - {FETO}_{2}} \right) \cdot} \\{{FETCO}_{2} - {FICO}_{2,{g\; 1}}}\end{bmatrix}}} = {\overset{.}{Q}\left( {{C\; \overset{\_}{v}{CO}_{2}} - {CaCO}_{2}} \right)}} & {{EQUATION}\mspace{14mu} 5}\end{matrix}$

Equation 5, based on the differential Fick equation, is a key testmathematical relationship from which other mathematical relationshipsare derived by solving for a test variable or an apparatus controllablevariable.

The results of solving EQUATION 5 for the mixed-venous concentration ofCO₂ and the pulmonary blood flow are shown in EQUATIONS 6.

$\begin{matrix}{{C\; \overset{\_}{v}{CO}_{2}} = {\frac{{\overset{.}{V}}_{g\; 1} \cdot \frac{310}{293} \cdot \begin{bmatrix}{\left( \frac{1 - {FICO}_{2,{g\; 1}} - {FIO}_{2,{g\; 1}}}{1 - {FETCO}_{2} - {FETO}_{2}} \right) \cdot} \\{{FETCO}_{2} - {FICO}_{2,{g\; 1}}}\end{bmatrix}}{\overset{.}{Q}} + {CaCO}_{2}}} & {{EQUATION}\mspace{14mu} 6a} \\{\mspace{79mu} {\overset{.}{Q} = \frac{{\overset{.}{V}}_{g\; 1} \cdot \frac{310}{293} \cdot \begin{bmatrix}{\left( \frac{1 - {FICO}_{2,{g\; 1}} - {FIO}_{2,{g\; 1}}}{1 - {FETCO}_{2} - {FETO}_{2}} \right) \cdot} \\{{FETCO}_{2} - {FICO}_{2,{g\; 1}}}\end{bmatrix}}{{C\; \overset{\_}{v}{CO}_{2}} - {CaCO}_{2}}}} & {{EQUATION}\mspace{14mu} 6b}\end{matrix}$

Similarly, the results of solving EQUATION 5 for the fractionalconcentration of CO₂ in the G1 gas and the flow rate of G1 gas are shownin EQUATIONS 7.

$\begin{matrix}{{FICO}_{2,{g\; 1}} = \frac{\begin{matrix}{{{\overset{.}{V}}_{g\; 1} \cdot \frac{310}{293} \cdot {FETCO}_{2} \cdot \left( {{FIO}_{2,{g\; 1}} - 1} \right)} +} \\{{\overset{.}{Q}\left( {{C\; \overset{\_}{v}{CO}_{2}} - {CaCO}_{2}} \right)}\left( {1 - {FETO}_{2} - {FETCO}_{2}} \right)}\end{matrix}}{{\overset{.}{V}}_{g\; 1} \cdot \frac{310}{293} \cdot \left( {{FETO}_{2} - 1} \right)}} & {{EQUATION}\mspace{14mu} 7a} \\{\mspace{79mu} {{\overset{.}{V}}_{g\; 1} = \frac{\overset{.}{Q}\left( {{C\; \overset{\_}{v}{CO}_{2}} - {CaCO}_{2}} \right)}{\frac{310}{293} \cdot \begin{bmatrix}{\left( \frac{1 - {{FIC}\; O_{2,{g\; 1}}} - {{FI}\; O_{2,{g\; 1}}}}{1 - {{FETC}\; O_{2}} - {{FET}O}_{2}} \right) \cdot} \\{{{FETC}\; O_{2}} - {{FIC}\; O_{2,{g\; 1}}}}\end{bmatrix}}}} & {{EQUATION}\mspace{14mu} 7b}\end{matrix}$

The Iterative NICO Method

The partial pressure of CO₂ in the arterial blood is assumed to be equalto the end-tidal partial pressure of CO₂ and then converted to aconcentration via the CO₂ dissociation curve of oxygenated whole blood[3,4]. This requires haemoglobin concentration ([HB]). [HB] ispreferably obtained from a blood gas analysis. If blood gas analysis isnot possible, [HB] can be measured transcutaneously. Alternatively, [HB]can be obtained from the normal published ranges for age/sex. End-tidalfractional concentrations can be converted to partial pressures bymultiplying the fractional concentrations by barometric pressure (PB)less the partial pressure of water vapour.

The amount of CO₂ in the lung is entirely determined by the alveolarventilation and the diffusion of CO₂ between the circulation and thealveolar space. If the pulmonary blood flow or the mixed-venousconcentration of CO₂ is known, the other can be calculated from thesteady state minute volume of expired CO₂ and arterial CO₂ concentration(EQUATIONS 6a,b). Therefore, the transfer rate of CO₂ between thecirculation and the alveolar space can be determined for any value ofend-tidal CO₂ as long as the pulmonary blood flow and mixed-venousconcentration of CO₂ remains unchanged. Correspondingly, following anacute change in end-tidal CO₂ from a previously steady value, if thealveolar ventilation can be controlled or measured, a temporary steadystate at the new end-tidal CO₂ (referred to as a test concentration) canbe maintained by delivering the inspired fraction of CO₂ and/or alveolarventilation required to exactly offset the influx from the circulation(EQUATIONS 7). This steady state can be maintained until themixed-venous CO₂ changes due to recirculation of the affected arterialblood.

Our algorithm recursively exploits this observation to measure thepulmonary blood flow. According to one embodiment, throughout eachiteration, the alveolar ventilation (={dot over (V)}_(g1)) is set with asequential gas delivery circuit. The fraction of O₂ in the G1 gas(FIO_(2,g1)) is not important, but should be held constant at a levelsufficient to maintain arterial oxygen saturation. The end-tidal gasesare measured by continuous real-time analysis of the expired gas.

In the baseline phase, the fractional concentration of CO₂ in the G1 gas(FICO_(2,g1,R)) is set and held constant. Although not necessary,FICO_(2,g1,R) is usually zero. The G1 gas flow during the rest phase({dot over (V)}_(g1,R)) is usually set to about 80% of the subjectstotal measured or estimated minute ventilation. In general, {dot over(V)}_(g1,R) should be low enough to permit rebreathing which at leastfills the subject's anatomical dead space, but high enough to preventhypercapnia. The baseline phase can be ended when end-tidal CO₂ isstable. Stability of end-tidal CO₂ can be determined by thestandard-deviation of end-tidal CO₂ measured over five breaths beingwithin ±2 mmHg, or if the difference between the largest and smallestend-tidal CO₂ measured over the last 5 breaths is within ±2 mmHg, or ifthe slope of the linear regression line passing through the end-tidalCO₂ of the last five breaths is less than ±0.5 mmHg/breath.Alternatively, the baseline period can be ended after predefined timehas elapsed and/or predefined number of breaths has occurred.

At the end of the baseline phase, the end-tidal CO₂ during the baselinephase (FETCO_(2,R)) is converted to an arterial concentration(CaCO_(2,R)). The end-tidal CO₂ from the last breath of the baselinephase can be used as FETCO_(2,R). Alternatively, FETCO_(2,R) can be theaverage of a number of breaths at the end of the baseline phase. Thebaseline minute volume of expired CO₂ ({dot over (V)}CO_(2,R)) iscalculated from EQUATION 4, using the average end-tidal O₂ (FETO_(2,R))measured during the baseline phase, {dot over (V)}_(g1,R),FICO_(2,g1,R), FIO_(2,g1), and FETCO_(2,R). A test value for an iteratedvariable, e.g. mixed-venous concentration of CO₂ is estimated fromEQUATION 6a using an estimate of the pulmonary blood flow ({dot over(Q)}_(est)), {dot over (V)}_(g1,R), FICO_(2,g1,R), FIO_(2,g1),FETCO_(2,R), FETO_(2,R), and CaCO_(2,R). Alternatively, a test value forpulmonary blood flow (a preferred iterated variable for convenience) isestimated starting from an estimate of the mixed-venous concentration ofCO₂ (C vCO_(2,est)) using EQUATION 6b with {dot over (V)}_(g1,R),FICO_(2,g1,R), FIO_(2,g1), FETCO_(2,R), FETO_(2,R), and CaCO_(2,R).

To transition from the baseline phase to the test phase, the inspiredfraction of CO₂ in the G1 gas is increased substantially for one bolusbreath, inducing a sharp increase in the end-tidal CO₂. The bolus breathmay optimally increase end-tidal CO₂ by approximately 10 mmHg to providesufficient measurement resolution and minimize discomfort to thepatient. The inspired fraction of CO₂ in the bolus breath(FICO_(2,g1,B)) required to elevate end-tidal CO₂ by approximately 10mmHg can be calculated using an approximation of the subject'sfunctional residual capacity (FRC), respiratory rate (RR), {dot over(V)}_(g1,R), and FETCO_(2,R) using EQUATION 8. The FRC can be estimatedor obtained from normal published ranges for the age, weight, and sex ofthe subject. Respiratory rate can be measured or estimated. For mostadults, FICO_(2,g1,B) of 15-20% should provide an adequate increase inend-tidal CO₂.

$\begin{matrix}{{FICO}_{2,{g\; 1},B} = \frac{{RR} \cdot \begin{bmatrix}\begin{matrix}\left( {{FETCO}_{2,R} + \frac{10}{{PB} - 47}} \right) \\{\left( {{FRC} + \frac{{\overset{.}{V}}_{g\; 1}}{RR}} \right) -}\end{matrix} \\{{FRC} \cdot {FETCO}_{2,R}}\end{bmatrix}}{{\overset{.}{V}}_{{g\; 1},R}}} & {{EQUATION}\mspace{14mu} 8}\end{matrix}$

The elevated end-tidal CO₂ (FETCO_(2,B)), and corresponding arterial CO₂(CaCO_(2,B)) measured in the exhalation immediately followinginspiration of the bolus are recorded. This recorded value representsthe test concentration of CO2 sought to be maintained in the test phase.Subsequently, a value for an apparatus controllable variable preferablyselected from the inspired fraction of CO₂ (FICO_(2,g1, T)) and G1 flowrate ({dot over (V)}_(g1,T)) during the test phase are set to try andmaintain end-tidal CO₂ at FETCO_(2,B). {dot over (V)}_(g1,T) can bechosen arbitrarily, but in general, {dot over (V)}_(g1,T) should be lowenough to permit rebreathing which at least fills the subjectsanatomical dead space. A test mathematical relationship solving forFICO2,g1 (EQUATION 7a), with {dot over (Q)}_(est), C vCO_(2,est), {dotover (V)}_(g1,T), FIO_(2,g1), FETCO_(2,B), FETO_(2,R), and CaCO_(2,B),can be used to calculate FICO_(2,g1,T) presumed to force a second steadystate of end-tidal CO₂ at FETCO_(2,B). Alternatively, FICO_(2,g1,T) canbe set arbitrarily within the limitations of the hardware and the testmathematical relationship solves for Vg1 (EQUATION 7b), with {dot over(Q)}_(est), C vCO_(2,est), FICO_(2,g1,T), FIO_(2,g1), FETCO_(2,B),FETO_(2,R), and CaCO_(2,B), can be used to calculate {dot over(V)}_(g1,T) presumed to force a second steady state of end-tidal CO₂ atFETCO_(2,B). This {dot over (V)}_(g1,T) and FICO_(2,g1,T) is delivereduntil recirculation is detected (described later), or for a predefinedlength of time presumed to be less than the recirculation time, or apredefined number of breaths presumed to occur before recirculation.

At the end of the test phase, the end-tidal CO₂ during the test phase(FETCO_(2,T)) is converted to an arterial concentration (CaCO_(2,T)).The end-tidal CO₂ from the last breath of the test phase can be used asa reference end tidal concentration (FETCO2,T). Alternatively,FETCO_(2,T) can be the average of values obtained for a number ofbreaths at the end of the test phase. The minute volume of expired CO₂during the test phase ({dot over (V)}CO_(2,T)) is calculated fromEQUATION 4, using the average end-tidal O₂ (FETO_(2,T)) measured duringthe test phase, {dot over (V)}_(g1,T), FICO_(2,g1,T), FIO_(2,g1), andFETCO_(2,T). Refined test values for pulmonary blood flow andmixed-venous CO₂ are recalculated ({dot over (Q)}_(calc), C vCO_(2calc))from EQUATIONS 3a1,b1 using {dot over (V)}CO_(2,R), CaCO_(2,R), {dotover (V)}CO_(2,T), and CaCO_(2T) or EQUATIONS 3a2,b2 using {dot over(Q)}_(est), C vCO_(2,est), FETCO_(2,B), and FETCO_(2,T). Subsequently,the system is returned to the baseline state.

This manoeuvre is repeated within successively refined test values forthe test variable utilizing either the calculated pulmonary blood flowof each test as the estimated pulmonary blood flow in the nextiteration, or the calculated mixed-venous CO₂ concentration as theestimated mixed-venous CO₂ concentration in the next iteration.

Selecting the Apparatus Controllable Variable and its Values:

Although {dot over (V)}_(g1,R) can be chosen arbitrarily, in general,{dot over (V)}_(g1,R) should be low enough to permit rebreathing whichat least fills the subject's anatomical dead space, but high enough toprevent hypercapnia. Although FICO_(2,g1,R) can be chosen arbitrarily,in general, there is not often a reason to deliver CO₂ in the baselinephase, and FICO_(2,g1, R) is generally set to zero. Although either {dotover (V)}_(g1,T) or FICO_(2,g1,T) can be set arbitrarily and the othervalue for the apparatus controllable variable calculated from EQUATIONS7a,b, it is simplest to set {dot over (V)}_(g1,T) equal to {dot over(V)}_(g1,R) during the test phase and calculate FICO_(2,g1,T) fromEQUATION 7a.

No O₂

It is pertinent to note that knowledge of inspired and end-tidal O₂ isonly required to implement the Haldane transform (EQUATION 4) whichgives a measure of expired volumes when only inspired volumes are known.In practise, the expired volumes are not significantly different thaninspired volumes. Where an oxygen analyzer is not present, the iterativealgorithm method described herein can be executed with a small loss inaccuracy using equations ending with (—O). (e.g. 7a-0, 7b-0, etc.)

Initiation and Convergence and Termination

The initial test value for the iterated variable, be it pulmonary bloodflow or mixed-venous CO₂, is taken as the middle of the normal publishedrange for the age, height, weight, and sex of the subject.Alternatively, the initial pulmonary blood flow or mixed-venous CO₂estimate can be arbitrary. Alternatively, the test value for pulmonaryblood flow can be estimated as 0.07 L/min/kg of subject body weight.Alternatively, the initial pulmonary blood flow or mixed-venous CO₂estimate can be obtained from a pervious execution of the recursivealgorithm. Alternatively, the initial test value for pulmonary bloodflow or mixed-venous CO₂ can be obtained from another measurementtechnique (thermodilution, mixed-venous blood gases). Alternatively, themixed-venous partial pressure of CO₂ can be estimated as 6 mmHg abovethe resting end-tidal CO₂ and converted to a concentration via the CO₂dissociation curve.

If the test value for pulmonary blood flow does not satisfy the testcriterion, the predicted transfer rate of CO₂ between the circulationand the alveolar space will also be in error. However, the minute volumeof expired of CO₂ in the test phase will exponentially equilibrate withthe flux across the blood-alveolar interface. As a result, the pulmonaryblood flow calculated in each test will be refined and better reflectthe actual pulmonary blood flow ({dot over (Q)}_(act)) than the ingoingtest value. Because the iterative algorithm is implemented recursively,and the estimated test value for the iterative variable is refined aftereach iteration to reflect the previously calculated test values, thealgorithm converges to the actual physiological parameters of thesubject.

The rate at which the calculated parameters converge to the actualparameters depends on how fast the end-tidal CO₂ approaches equilibriumin the test phase. The derivative of an exponential function is largestat the start and vanishes with time. Therefore, a substantial refinementin the estimated parameters occurs in the breaths before recirculation.As a result, the calculated parameters at the end of each test aresignificantly more accurate than the previous estimates.

Testing is optionally terminated when the difference in pulmonary bloodflow calculated between subsequent tests differs in magnitude less thana user-definable threshold. Optionally, the algorithm can be continuedindefinitely. Optionally, the algorithm can be executed for a predefinednumber of iterations. All of these options satisfy a test criterion.

Detection of Recirculation

The pulmonary recirculation time varies between individuals, and withinthe same individual in different hemodynamic states. Indeed, thereported interval before recirculation occurs differs significantlyamongst investigators.

We detect the occurrence of recirculation by analysis of the time courseof the end-tidal CO₂ during the test phase. Prior to recirculation, theend-tidal CO₂ approaches a steady value exponentially—the absolutedifference between consecutive end-tidal measurements decreases as thetest proceeds. Recirculation causes a deviation from this asymptoticapproach, detectable as an increase in the difference betweenconsecutive end-tidal CO₂ measurements. Accordingly, in our method, thetest proceeds as long as the magnitude of the difference betweenconsecutive end-tidal CO₂ measurements is decreasing.

More specifically, let FETCO_(2,T,x) be the end-tidal CO₂ of a breathduring the test phase, and FETCO_(2,T,x−1) and FETCO_(2,T,x+1) be thebreaths immediate before and after. The last breath before recirculationis the first test breath for which:

FETCO_(2,T,x)−FETCO_(2,T,x−1)|<|FETCO_(2,T,x+1)−FETCO_(2,T,x)  EQUATION9

Apparatus

According to one embodiment of a gas delivery system, the systemapparatus is shown in FIG. 1. It consists of a gas blender 22, asequential gas delivery circuit 26, gas analyzers for oxygen 16 andcarbon dioxide 18, a pressure transducer 14, a computer 8 includingsoftware 10 (which is optionally embodied a computer program product)that works the gas blender 22 to request gas flows and with the gasanalyzers 16 and 18, pressure transducer 14 and input devices formeasured or estimated physiological parameters 36 and algorithm settings34 to obtain inputs as contemplated herein. The gas blender 22 may beconnected to three pressurized gas tanks 32. The gas blender optionallycontains three rapid flow controllers (not shown) capable of deliveringaccurate mixes of three source gases, optionally comprised of CO₂, O₂,and N₂ to the circuit. The concentrations of CO₂, O₂, and N₂ in thesource gases must be such that they can produce the blends required tocarry out the algorithm. Pure CO₂, O₂, and N₂ are one option. The gasanalyzers 18 and 16 measure the fractional concentrations of CO₂ and O₂at the mouth throughout the breath. The pressure transducer 14 is usedfor end-tidal detection. The computer runs a software implementation ofa pulmonary blood flow measurement algorithm and demands the requiredmixtures from the blender 22. The monitor may display the real-timecapnograph, oxigraph, pulmonary blood flow, and mixed-venousconcentration of CO₂.

{dot over (Q)}_(calc)={dot over (Q)}_(est) +k(FETCO_(2,B)−FETCO_(2,T))k>0  EQUATION 3a2

C v CO_(2,calc)=C v CO_(2,est) −k(FETCO_(2,B)−FETCO_(2,T)) k>0  EQUATION3b2

DESCRIPTION OF FIGURES FIG. 4

1 The initial pulmonary blood flow or mixed-venous CO₂ estimate is takenas the middle of the normal published range for the age, height, weight,and sex of the subject. Alternatively, the initial pulmonary blood flowor mixed-venous CO₂ estimate can be arbitrary. Alternatively, pulmonaryblood flow can be estimated as 0.07 L/min/kg of subject body weight.Alternatively, the initial pulmonary blood flow or mixed-venous CO₂estimate can be obtained from a pervious execution of the recursivealgorithm. Alternatively, the initial pulmonary blood flow ormixed-venous CO₂ estimate can be obtained from another measurementtechnique (thermodilution, mixed-venous blood gases). Alternatively, themixed-venous partial pressure of CO₂ can be estimated as 6 mmHg abovethe resting end-tidal CO₂ and converted to a concentration via the CO₂dissociation curve.

2 In the baseline phase, the fractional concentration of CO₂ in the G1gas (FICO_(2,g1,R)) is set and held constant. Although not necessary,FICO_(2,g1,R) is usually zero. The G1 gas flow during the rest phase({dot over (V)}_(g1,R)) is usually set to about 80% of the subjectstotal measured or estimated minute ventilation. In general, {dot over(V)}_(g1,R) should be low enough to permit rebreathing which at leastfills the subject's anatomical dead space, but high enough to preventhypercapnia.

3 The baseline phase can be ended when end-tidal CO₂ is stable.Stability of end-tidal CO₂ can be determined by the standard-deviationof end-tidal CO₂ measured over five breaths being within ±2 mmHg, or ifthe difference between the largest and smallest end-tidal CO₂ measuredover the last 5 breaths is within ±2 mmHg, or if the slope of the linearregression line passing through the end-tidal CO₂ of the last fivebreaths is less than ±0.5 mmHg/breath. Alternatively, the baselineperiod can be ended after predefined time has elapsed and/or predefinednumber of breaths has occurred.

4 At the end of the baseline phase, the end-tidal CO₂ during thebaseline phase (FETCO_(2,R)) is converted to an arterial concentration(CaCO_(2,R)). The end-tidal CO₂ from the last breath of the baselinephase can be used as FETCO_(2,R). Alternatively, FETCO_(2,R) can be theaverage of a number of breaths at the end of the baseline phase.

5 The baseline minute volume of expired CO₂ ({dot over (V)}CO_(2,R)) iscalculated from EQUATION 4, using the average end-tidal O₂ (FETO_(2,R))measured during the baseline phase, {dot over (V)}_(g1,R),FICO_(2,g1,R), FIO_(2,g1), and FETCO_(2,R).

6 The mixed-venous concentration of CO₂ is estimated from EQUATION 6ausing an estimate of the pulmonary blood flow ({dot over (Q)}_(est)),{dot over (V)}_(g1,R), FICO_(2,g1,R), FIO_(2,g1), FETCO_(2,R),FETO_(2,R), and CaCO_(2,R). Alternatively, the pulmonary blood flow isestimated starting from an estimate of the mixed-venous concentration ofCO₂ (C vCO_(2,est)) using EQUATION 6b with {dot over (V)}_(g1,R),FICO_(2,g1,R), FIO_(2,g1), FETCO_(2,R), FETO_(2,R), and CaCO_(2,R).

7 To transition from the baseline phase to the test phase, the inspiredfraction of CO₂ in the G1 gas is increased substantially for one bolusbreath, inducing a sharp increase in the end-tidal CO₂. In oneembodiment, the bolus breath increases end-tidal CO₂ by approximately 10mmHg to provide sufficient measurement resolution and minimizediscomfort to the patient. The inspired fraction of CO₂ in the bolusbreath (FICO_(2,g1,B)) required to elevate end-tidal CO₂ byapproximately 10 mmHg can be calculated using an approximation of thesubject's functional residual capacity (FRC), respiratory rate (RR),{dot over (V)}_(g1,R), and FETCO_(2,R) using EQUATION 8. The FRC can beestimated or obtained from normal published ranges for the age, weight,and sex of the subject. Respiratory rate can be measured or estimated.For most adults, FICO_(2,g1, B) of 15-20% should provide an adequateincrease in end-tidal CO₂.

$\begin{matrix}{{FICO}_{2,{g\; 1},B} = \frac{{RR} \cdot \begin{bmatrix}\begin{matrix}\left( {{FETCO}_{2,R} + \frac{10}{{PB} - 47}} \right) \\{\left( {{FRC} + \frac{{\overset{.}{V}}_{g\; 1}}{RR}} \right) -}\end{matrix} \\{{FRC} \cdot {FETCO}_{2,R}}\end{bmatrix}}{{\overset{.}{V}}_{{g\; 1},R}}} & {{EQUATION}\mspace{14mu} 8}\end{matrix}$

The elevated end-tidal CO₂ (FETCO_(2,B)), and corresponding arterial CO₂(CaCO_(2,B)) measured in the exhalation immediately followinginspiration of the bolus are recorded. This recorded value representsthe test concentration of CO₂ sought to be maintained in the test phase.

9 Subsequently, the inspired fraction of CO₂ (FICO_(2,g1,T)) and G1 flowrate ({dot over (V)}_(g1,T)) during the test phase are set to try andmaintain end-tidal CO₂ at FETCO_(2,B). {dot over (V)}_(g1,T) can bechosen arbitrarily, but in general, {dot over (V)}_(g1,T) should be lowenough to permit rebreathing which at least fills the subject'sanatomical dead space. EQUATION 7a, with {dot over (Q)}_(est), CvCO_(2,est), {dot over (V)}_(g1,T), FIO_(2,g1), FETCO_(2,B), FETO_(2,R),and CaCO_(2,B), can be used to calculate FICO_(2,g1,T) presumed to forcea second steady state of end-tidal CO₂ at FETCO_(2,B). Alternatively,FICO_(2,g1,T) can be set arbitrarily within the limitations of thehardware and EQUATION 7b, with {dot over (Q)}_(est), C vCO_(2,est),FICO_(2,g1,T), FIO_(2,g1), FETCO_(2,B), FETO_(2,R), and CaCO_(2,B), canbe used to calculate {dot over (V)}_(g1,T) presumed to force a secondsteady state of end-tidal CO₂ at FETCO_(2,B).

This {dot over (V)}_(g1,T) and FICO_(2,g1,T) is delivered untilrecirculation is detected (described later), or for a predefined lengthof time presumed to be less than the recirculation time, or a predefinednumber of breaths presumed to occur before recirculation.

11 At the end of the test phase, the end-tidal CO₂ during the test phase(FETCO_(2,T)) is converted to an arterial concentration (CaCO_(2,T)).The end-tidal CO₂ from the last breath of the test phase can be used asFETCO_(2,T)Alternatively, FETCO_(2,T) can be the average of a number ofbreaths at the end of the test phase.

12 The minute volume of expired CO₂ during the test phase ({dot over(V)}CO_(2,T)) is calculated from EQUATION 4, using the average end-tidalO₂ (FETO_(2,T)) measured during the test phase, {dot over (V)}_(g1,T),FICO_(2,g1,T), FIO_(2,g1), and FETCO_(2,T). Pulmonary blood flow andmixed-venous CO₂ are recalculated ({dot over (Q)}_(calc), C vCO_(2calc))from EQUATIONS 3a1,b1 using VCO_(2,R), CaCO_(2,R), VCO_(2,T), andCaCO_(2,T) or EQUATIONS 3a2,b2 using {dot over (Q)}_(est), CvCO_(2,est), FETCO_(2,B), and FETCO_(2,T). Subsequently, the system isreturned to the baseline state.

This manoeuvre is repeated utilizing either the calculated pulmonaryblood flow of each test as the estimated pulmonary blood flow in thenext iteration, or the calculated mixed-venous CO₂ concentration as theestimated mixed-venous CO₂ concentration in the next iteration.

13 Testing is terminated when the difference in pulmonary blood flowcalculated between subsequent tests differs in magnitude less than auser-definable threshold. Optionally, the algorithm can be continuedindefinitely. Optionally, the algorithm can be executed for a predefinednumber of iterations.

FIG. 1

According to one embodiment of a gas delivery system, the systemapparatus is shown in FIG. 1. It consists of a gas blender 22, asequential gas delivery circuit 26, gas analyzers for oxygen 16 andcarbon dioxide 18, a pressure transducer 14, a computer 8 includingsoftware 10 (which is optionally embodied a computer program product)that works the gas blender 22 to request gas flows and with the gasanalyzers 16 and 18, pressure transducer 14 and input devices formeasured or estimated physiological parameters 36 and algorithm settings34 to obtain inputs as contemplated herein. The gas blender 22 may beconnected to three pressurized gas tanks 32. The gas blender optionallycontains three rapid flow controllers (not shown) capable of deliveringaccurate mixes of three source gases, optionally comprised of CO₂, O₂,and N₂ to the circuit. The concentrations of CO₂, O₂, and N₂ in thesource gases must be such that they can produce the blends required tocarry out the algorithm. Pure CO₂, O₂, and N₂ are one option. The gasanalyzers 18 and 16 measure the fractional concentrations of CO₂ and O₂at the mouth throughout the breath. The pressure transducer 14 is usedfor end-tidal detection. The computer runs a software implementation ofa pulmonary blood flow measurement algorithm and demands the requiredmixtures from the blender 22. The monitor may display the real-timecapnograph, oxigraph, pulmonary blood flow, and mixed-venousconcentration of CO₂.

Other inputs to the algorithm include an initial estimate of pulmonaryblood flow or mixed-venous CO₂ 36, and termination criteria for thealgorithm 34.

FIG. 5 Panel A

In FIG. 5 a (Panel A), three iterations of the recursive algorithmshowing convergence of the calculated pulmonary blood flow to the actualpulmonary blood flow starting from an incorrect estimate. As shown, ifthe estimated pulmonary blood flow is incorrect, the predicted transferrate of CO₂ between the circulation and the alveolar space will also bein error. However, the minute volume of expired of CO₂ in the test phasewill exponentially equilibrate with the flux across the blood-alveolarinterface. As a result, the pulmonary blood flow calculated in each testwill better reflect the actual pulmonary blood flow ({dot over(Q)}_(act)) than the ingoing estimate. Because this procedure isimplemented recursively, and the estimated parameters updated after eachiteration to reflect the previously calculated values, the algorithmconverges to the actual physiological parameters of the subject.

The rate at which the calculated parameters converge to the actualparameters depends on how fast the end-tidal CO₂ approaches equilibriumin the test phase. The derivative of an exponential function is largestat the start and vanishes with time. Therefore, a substantial refinementin the estimated parameters occurs in the breaths before recirculation.As a result, the calculated parameters at the end of each test aresignificantly more accurate than the previous estimates.

Panel B

FIG. 5B (Panel B) shows that (a) if the estimate of pulmonary blood flowis higher than the actual pulmonary blood flow, the end-tidal CO₂ in thetest phase drifts exponentially upwards; (b) if the estimate ofpulmonary blood flow is lower than the actual pulmonary blood flow, theend-tidal CO₂ in the test phase drifts exponentially downwards; (c) ifthe estimate of pulmonary blood flow is approximately equal to than theactual pulmonary blood flow, the end-tidal CO₂ in the test phase remainsconstant. It also shows how recirculation may be detected by analysis ofthe time course of the end-tidal CO₂ during the test phase. Prior torecirculation, the end-tidal CO₂ approaches a steady valueexponentially—the absolute difference between consecutive end-tidalmeasurements decreases as the test proceeds. Recirculation causes adeviation from this asymptotic approach, detectable as an increase inthe difference between consecutive end-tidal CO₂ measurements.Mathematically, this is shown in equation 9.

REFERENCES

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1-29. (canceled)
 30. A method of controlling a gas delivery apparatus todeliver a test gas (TG) for non-invasively determining a subject'spulmonary blood flow comprising the steps of: (a) Using an iterativealgorithm to control at least one apparatus controllable variable totest one or more test values for an iterated variable by: A) Obtaininginput of a steady state value of an end tidal test gas concentration anda corresponding value of at least one apparatus controllable variablefor use in the iterative algorithm; B) providing an inspiredconcentration of a test gas that achieves a test concentration of thetest gas in the subject's end tidal exhaled gas; C) using a test valueof the iterated variable in the iterative algorithm to set the gasdelivery apparatus to deliver, for at least one series of inspiratorycycles, an inspiratory gas comprising a test gas that is computed tomaintain the test concentration of the test gas in the subject's endtidal exhaled gas; D) obtaining input comprising measurements of endtidal concentrations of test gas for expiratory cycles corresponding tothe at least one series of inspiratory cycles and a corresponding valueof at least one apparatus controllable variable for use in the iterativealgorithm; E) using at least one measurement obtained in step D) as areference end tidal concentration value to generate at least one of thefollowing outputs: (1) the test value satisfies a test criterion; (2) arefined test value; wherein the reference end tidal concentration is asurrogate steady state value and the reference end tidal concentrationis used to refine the test value; (b) If output (1) is not obtained,repeating step (a) as necessary at least until output (1) is obtained;and (c) If output (1) is obtained, outputting a value for pulmonaryblood flow which, based on the test criterion, sufficiently represents asubject's true pulmonary blood flow.
 31. A method according to claim 30,wherein the reference end tidal concentration is the last measurementobtained prior to a recirculation or an average of such lastmeasurements.
 32. A method according to claim 31, wherein the test gasis carbon dioxide.
 33. A method according to claim 30, wherein iterativealgorithm is characterized in that it defines a mathematicalrelationship between the at least one apparatus controllable variable,the iterated variable and the end tidal concentration of test gasattained by setting the apparatus controllable variable, such that theiterative algorithm is determinative of whether iteration on the testvalue satisfies a test criterion or iteratively generates aprogressively refined test value.
 34. A method according to claim 30,wherein the iterative algorithm employs a test mathematical relationshipbased on the Fick equation.
 35. A method according to claim 34, whereinthe refined test value is ascertained based on the differential Fickequation.
 36. A method according to claim 34, wherein the refined testvalue is ascertained based on equation 3a2 or equation 3b2.
 37. A methodaccording to claim 34, wherein the iterative algorithm employs equation5 or equation 5-0.
 38. A method according to claim 30, wherein theapparatus controllable variable is the inspired concentration of testgas in the inspiratory gas.
 39. A method according to claim 30, whereinthe apparatus controllable variable is rate of flow of test gascontaining inspiratory gas into the circuit, where the rate of flow isdeterminative of the alveolar ventilation.
 40. A method according toclaim 30, wherein the iterated variable is pulmonary blood flow.
 41. Amethod according to claim 30, wherein the iterated variable is avariable determined by pulmonary flow from which pulmonary blood flowcan be mathematically computed.
 42. A method according to claim 39,wherein the iterated variable is a mixed venous concentration of testgas.
 43. A gas delivery system adapted to deliver a test gas (TG) fornon-invasively determining a subject's pulmonary blood flow comprising:A gas delivery apparatus; A control system for controlling the gasdelivery apparatus including at least one apparatus controllablevariable to test one or more test values for a iterated variable, thecontrol system comprising a computer for executing an iterativealgorithm, the gas delivery system including means for: A) Obtaininginput of a steady state value of an end tidal test gas concentration anda corresponding value of at least one apparatus controllable variablefor use in the iterative algorithm; B) providing an inspiredconcentration of a test gas that achieves a test concentration of thetest gas in the subject's end tidal exhaled gas; C) using a test valueof the iterated variable in an iterative algorithm to set the gasdelivery apparatus to deliver, for at least one series of inspiratorycycles, an inspiratory gas comprising a test gas that is computed tomaintain the test concentration of the test gas based a test value ofthe iterated variable; D) obtaining input comprising measurements of endtidal concentrations of test gas for expiratory cycles corresponding tothe at least one series of inspiratory cycles; E) using at least onemeasurement obtained in step C) as a reference end tidal concentrationvalue to generate at least one of the following outputs: (1) the testvalue satisfies the test criterion; (2) a refined test value; whereinthe reference end tidal concentration is a surrogate steady state valueand is used to generate the refined test value: wherein the iterativealgorithm uses at least one apparatus controllable variable toiteratively test one or more of test values for the iterated variablebased on the following criteria: If output (1) is not obtained,repeating step (B) to (E) as necessary at least until output (1) isobtained; and If output (1) is obtained, outputting a value forpulmonary blood flow which, based on the test criterion, sufficientlyrepresents a subject's true pulmonary blood flow.
 44. A gas deliverysystem according to claim 43, wherein the gas delivery apparatuscomprises at least one input port for receiving an inspiratory gascontaining the test gas, at least one output port for connection to abreathing circuit and a flow controller for controlling the rate of flowof the inspiratory gas.
 45. A gas delivery system according to claim 43,wherein the computer is CPU.
 46. A gas delivery system according toclaim 43, wherein reference end tidal concentration is the lastmeasurement obtained prior to a recirculation or an average of such lastmeasurements.
 47. A gas delivery system according to claim 43, whereinthe test gas is carbon dioxide.
 48. A gas delivery system according toclaim 43, wherein iterative algorithm is characterized in that itdefines a mathematical relationship between the at least one apparatuscontrollable variable, the iterated variable and the end tidalconcentration of test gas attained by setting the apparatus controllablevariable, such that the iterative algorithm is determinative of whetheriteration on the test value satisfies a test criterion or iterativelygenerates a progressively refined test value.
 49. A gas delivery systemaccording to claim 48, wherein the iterative algorithm employs a testmathematical relationship based on the Fick equation.
 50. A gas deliverysystem according to claim 48, wherein the iterative algorithm employsequation 5 or equation 5-0.
 51. A gas delivery system according to claim43, wherein the apparatus controllable variable is the inspiredconcentration of test gas in the inspiratory gas.
 52. A gas deliverysystem according claim 43, wherein the apparatus controllable variableis rate of flow of test gas containing inspiratory gas into the circuit,where the rate of flow is determinative of the alveolar ventilation. 53.A gas delivery system according to claim 43, wherein the iteratedvariable is pulmonary blood flow.
 54. A gas delivery system according toclaim 43, wherein the iterated variable is a variable determined bypulmonary flow from which pulmonary blood flow can be mathematicallycomputed.
 55. A gas delivery system according to claim 43, wherein theiterated variable is a mixed venous concentration of test gas.
 56. Acomputer program product comprising a non-transitory computer readablemedium encoded with program code for controlling the operation of gasdelivery apparatus including at least one apparatus controllablevariable, the program code including code for iteratively generating andevaluating test values of a iterated variable based on an iterativealgorithm in order output a test value of the iterated variable thatmeets a test criterion including program code for: A) Obtaining input ofa steady state value of an end tidal test gas concentration and acorresponding value of at least one apparatus controllable variable foruse in the iterative algorithm; B) providing an inspired concentrationof a test gas that achieves a test concentration of the test gas in thesubject's end tidal exhaled gas and using the test value of the iteratedvariable in the iterative algorithm to set the gas delivery apparatus todeliver, for at least one series of inspiratory cycles, an inspiratorygas comprising a test gas that is computed to maintain the testconcentration of the test gas; C) obtaining input comprisingmeasurements of end tidal concentrations of test gas for expiratorycycles corresponding to the at least one series of inspiratory cycles;D) using at least one measurement obtained in step C) as a reference endtidal concentration value to generate at least one of the followingoutputs: (3) the test value satisfies the test criterion; (4) a refinedtest value; wherein the reference end tidal concentration is a surrogatesteady state value and is used to obtain the refined test value; whereinthe iterative algorithm uses at least one apparatus controllablevariable to iteratively test one or more of test values for the iteratedvariable based on the following criteria: If output (1) is not obtained,repeating step (B) to (D) as necessary at least until output (1) isobtained; and If output (1) is obtained, outputting a value forpulmonary blood flow which, based on the test criterion, sufficientlyrepresents a subject's true pulmonary blood flow.